When I changed my name I just wrote that I was trans and that I was changing my name to one that I better identified with and better reflected my real sex. Personally, I think it's a good idea to give them a reason, though I doubt anyone would refuse you a name change because of the reason/failure to give a clear one. As long as the rest of the info matches up, that's all they care about. At least in Canada, but then again we don't have to go to court to do it either, just fill in the application and mail it in. As long as all the info is correct they grant you the change.